An alternative approach for proving the NP-hardness of optimization problems

•A new approach for proving the NP-hardness of optimization problems is proposed.•The new approach includes the “classical” approach as a special case.•NP-hardness of a problem is proved, for which the classical approach is not applicable.•Polynomially solvable problem with NP-hard computable objective is formulated.

We provide a new reduction-based approach for proving the NP-hardness of optimization problems and establish that it includes the “classical” approach as a special case. We apply our alternative approach to prove the NP-hardness of a problem for which the classical approach is not applicable. Besides, we construct a special case of the problem with the property that finding an optimal element takes polynomial time despite that computing the objective function values is NP-hard.